This book offers a broad survey of all information made public - from 1993 until today - on keystream sequence generators based on irregular decimation, which are referred to as shrinking generators. Starting with an overview of cryptography, it describes each type of generator - shrinking, self-shrinking, modified self-shrinking, generalized self-shrinking and the DECIM algorithm - with examples and references. Further, the book discusses several attacks on these generators and applications. It concludes by demonstrating how the output sequences can be modeled by means of different families of one-dimensional cellular automata, rendering the generators vulnerable to attacks. Intended for researchers and graduate students, the book will hopefully inspire them to search for more details on this family of generators and to address the open problems in this field. .